Finite Group Databasebeta

C32×#13095331 #28356656

order13851
automorphism?
homologyAbelianization (H1) = C35 · Schur multiplier (H2) = C39

Aliases

direct productC32×#13095331

Splittings

SylowC19 ⋊ C32×#737

Subgroups

subgroupG/H
centerC33C32×C19⋊C3
commutator, cosocleC3×C19C35
FrattiniC3C34×C19⋊C3
Fitting, prime radicalC32×C19×H(3,𝔽3)C3
socleC33×C19C33
hypercenterC32×H(3,𝔽3)C19⋊C3
hypocenterC19C32×#737
LCSG ▷ C3×C19 ▷ C19
UCSC1 ◁ C33 ◁ C32×H(3,𝔽3)

5804 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4617

Conjugacy classes & character table

891 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13851, 4020);